Portfolio investment analysis on the basis of the blacklitterman model

AutorAlexey G. Isavnin - Damir R. Galiev - Anton N. Karamyshev - Ilnur I. Makhmutov
CargoKazan Federal University. e-mail: antonkar2005@yandex.ru. Tel.: +7-960-067-65-50
Páginas266-281
Periódico do Núcleo de Estudos e Pesquisas sobre Gênero e Direito
Centro de Ciências Jurídicas - Universidade Federal da Paraíba
V. 8 - Nº 06 - Ano 2019 – Special Edition
ISSN | 2179-7137 | http://periodicos.ufpb.br/ojs2/index.php/ged/index
266
PORTFOLIO INVESTMENT ANALYSIS ON THE BASIS OF THE
BLACK-LITTERMAN MODEL
Alexey G. Isavnin1
Damir R. Galiev2
Anton N. Karamyshev3
Ilnur I. Makhmutov4
Abstract: The works of Markowitz,
Tobin, Sharp in the field of portfolio
investment theory are awarded the Nobel
Prize in economics. The popularity of
these models is explained by their
mathematical simplicity and logical
harmony. But these models require
accurate knowledge of the statistical
features of assets and use assumptions
about ideal market behavior. A large
number of questions immediately arise
on how to evaluate the input parameters
of these models in the practical use of
these models. In the Black-Litterman
model, an attempt is made to combine
the theory of equilibrium in the capital
market with the subjective opinions of
analysts regarding the expected return on
assets and their relationship to each
other. The Black-Litterman model
1 Kazan Federal University. e-mail:
antonkar2005@yandex.ru. Tel.: +7-960-067-65-50
2 Kazan Federal University. e-mail:
antonkar2005@yandex.ru. Tel.: +7-960-067-65-50
3 Kazan Federal University. e-mail:
antonkar2005@yandex.ru. Tel.: +7-960-067-65-50
4 Kazan Federal University. e-mail:
antonkar2005@yandex.ru. Tel.: +7-960-067-65-50
makes it possible to combine the theory
of market equilibrium and the subjective
opinions of investors about asset
behavior in the market. The result is a
diversified portfolio with a subjective
opinion on the situation. This model is a
new word in portfolio theory, which is
relatively complex and focused on
professionals. Due to the Bayesian
approach, it is formed a new, more
realistic mixed estimate of expected
returns, taking into account the opinions
of expert analysts. In Western literature,
the Black-Litterman model is recognized
as an important and powerful tool in the
process of portfolio investment
management. In particular, the work
discusses in detail the issues of
collecting, analyzing and preparing
expert opinions. The ability to take into
Periódico do Núcleo de Estudos e Pesquisas sobre Gênero e Direito
Centro de Ciências Jurídicas - Universidade Federal da Paraíba
V. 8 - Nº 06 - Ano 2019 – Special Edition
ISSN | 2179-7137 | http://periodicos.ufpb.br/ojs2/index.php/ged/index
267
account the expert assessments is the
main advantage of this model over all
others.
Keywords: Black-Litterman model,
portfolio investment, analysis,
uncertainty, risk, profitability.
1 Introduction
The main goal of this work is to
disclose the principles of optimal and
meaningful management of a securities
portfolio using one of the latest
achievements in the field of portfolio
theory - the Black-Litterman model, -
modernization of existing solutions and
software development to solve such
problems.
2 Text Of Article
Until recently, modern portfolio
theory formed by G. Markowitz as far
back as 1952 remained almost the only
quantitative method for solving the
portfolio analysis problem [2]. Before
proceeding to the Black-Litterman
model, we briefly consider the
Markowitz model and its shortcomings.
Let there be n types of assets from which
the investor can form a portfolio. Capital
is distributed between assets in shares
=
=n
i
iii xxx
1
1,10, . Assets are
characterized by efficiencies Ri, which
are random variables with known
mathematical expectations MRi=mi, and
covariance matrix
),cov( ji RR=Σ .
The Markowitz problem is formulated as
follows (1):
nixmxmx
xx
i
n
i
pii
n
i
i
T
x
,1,0,,1
min
11
==
Σ
==
(1)
Although the Harry Markowitz
model may seem attractive and well-
grounded from a theoretical point of
view, a number of problems arise in its
practical application [8, 11, 12].
Application of the Markowitz model in
the Russian market also showed its
inconsistency [2].
The main disadvantages of the
Markowitz model are as follows:

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